If the planes `vecr.(hati+hatj+hatk)=q_(1),vecr.(hati+2ahatj+hatk)=q_(2)andvecr.(ahati+a^(2)hatj+hatk)=q_(3)` intersect in a line, then the value of `a` is

Options

A. 1
B. `1//2`
C. 2
D. 0

Answer

a, b

Explanation

`vecr*vec(n_1)=vec(q_1) and vecr*vec(n_2)=vecq_(2), vecr*vecn_(3)= vecq_(3) `
intersect in a line if `[vecn_(1) vecn_(2) vecn_(3)]=0`. So,
`" "|{:(1,,1,,1),(1,,2a,,1),(a,,a^(2),,1):}|=0`
or `" "2a-a^(2)-1+a+a^(2)-2a^(2)=0`
or `" "2a^(2)-3a+1=0`
or `" "a=1//2, 1`